We need a Secretary of Education who has classroom teaching experience beyond grade 5 and has administered a middle or high school for at least a couple of years or so. This experience gives teaching faculty a chance to understand and tell us a little bit about a candidate’s supervisory style. No need for a particular ethnicity or race or gender. We’ve tried using all these sociocultural criteria, especially in our major cities. But no criterion has worked for most kids.
Are recent nation-wide riots, looting, and arson all in large part expressions of our frustration with and rage at seemingly failed or ineffective educational institutions? We haven’t tried yet to make other institutions or agencies for public health or safety responsible for educating the nation’s children. We need to try, because it is clear that public educational facilities are no longer capable of educating our young or producing productive citizens.
There are several questions we should ask ourselves to try to understand the basis for the many waves of rioting in our major cities in recent years, most recently Portland, Oregon.
- Why haven’t our educational institutions found effective remedial strategies for low-achieving students by now—over 50 years after the first federal grants to low-income schools and communities in ESEA in 1965?
- Do schools in undeveloped or under-developed countries produce similar or lower levels of performance on the TIMSS, PIRLS, and PISA tests given to comparable children of low-income parents in this country on these tests? These have been the chief international tests available for our states to participate in.
- What are the average scores for each demographic group in countries with many non-dominant population groups as in the USA, Australia, Canada, and Singapore?
Maybe education researchers have looked at the wrong things or not asked the right questions, such as:
- How much reading or other homework have teachers assigned their students in K-12?
- How many parents check the time their children go to bed every night and how much they read or practice every day?
- Why have pre-schools on average, or after-school programs extending school teaching hours, failed to create equity among demographic groups in the K-12 school population?
- Why has the use of literary texts and curriculum-aligned textbooks whose subject matter and vocabulary have been reduced in difficulty (such as in recent Afrocentric curricula like 1619 ) failed to boost minority scores?
Who could be recommended for Secretary of Education? Perhaps all parents would agree that such a person needs classroom teaching experience, knows well at least one of the subjects typically taught in K-12, and has read a lot and writes well. All parents might also agree that it would be useful to have a Secretary of Education who knows beginning reading research as well as research on beginning arithmetic education.
It is partially Congress’s fault that a regularly increasing amount of federal and state money in over fifty years hasn’t helped low-income minorities in education. Congress hasn’t targeted the areas of influence on school achievement noted in the 1966 Coleman Report and the 1965 Moynihan Report. The two most comprehensive reports on differences in academic achievement in this country found family background more influential than schools and teachers. In other words, social factors were more important than educational interventions. The Coleman Report also noted, based on a test its authors devised, that the teachers of non-black students had greater knowledge and verbal skills than did the teachers of black children. It made no specific recommendations, but it is not difficult to infer that low-achieving students would benefit from academically stronger teachers. Recent information can be found here. It is clear that whatever our public schools have done since WWII hasn’t increased achievement in low-achieving students.
In recent years, many educators have promoted school choice, especially via charter schools, as ways to strengthen low-achieving students. But school choice may be useful to promote only if curriculum choices and the portability of funds for individual students are allowed. Letting public money be used for children in schools their parents want them to attend (whether private religious or secular schools), without a mandate to use Common Core-aligned standards, tests, textbooks, and teachers trained in Common Core-aligned material may finally enable school choice to be the motivational mechanism its supporters envisioned. The benefits of school choice are unlikely to emerge within the context of a Common Cored curriculum.
To ensure civic equity, it is likely we need to nationalize civic education—the major subject where common historical and contemporary knowledge across schools would make sense such as the basic principles in the US Constitution. Some educators have strongly supported the use of some of the questions on our naturalization quiz as the basis for a high school graduation test. But to ensure diverse voices in history and geography at the classroom level, teachers could invite each parent of students in their grades 3-8 classes to recommend a good ethnic story/poem to discuss in class, with close relatives invited to attend and participate.
The road to effective education is paved with local financial control and parent choice. No federal funding or programs. We should acknowledge that high schools cannot prepare all kids for college and that all students do not want to go to college. High schools should establish several sets of standards rather than a single set of academic standards and let students take programs or course sequences that appeal to them.
For a discussion of effective standards and K-12 curricula and tests, listen to Ingrid Centurion’s interview with me about education.
Editor’s Note: At long last!! This is Chapter 20, the last chapter in this series called “Out on Good Behavior: Teaching Math While Looking Over Your Shoulder” by Barry Garelick, a second-career math teacher in California. He has written articles on math education that have appeared in The Atlantic, Education Next, Education News and AMS Notices. He is also the author of three books on math education. Says Mr. Garelick: “I thank all my faithful readers for staying with this til the end. The book will be out in the fall. That said, there will be no book tour.” The previous chapters can be found here: Chapter 1 , Chapter 2 , Chapter 3 , Chapter 4 , Chapter 5, Chapter 6, Chapter 7, Chapter 8, Chapter 9, Chapter 10, Chapter 11, Chapter 12, Chapter 13, Chapter 14, Chapter 15 and Chapter 16, Chapter 17, Chapter 18, and Chapter 19.
Chapter 20 Out on Good Behavior, and a Final Narrative
My meetings with Diane during my second year at Cypress had taken place once a week, initially at a coffee shop near the school. When that proved to be too noisy we moved to my classroom. The day finally came when all electronic checklists had been filled out and discussions ended.
The potential for ending our discussions reminded me of a conversation I had in the Math 7 class regarding how you cannot divide by zero, nor zero by zero. I asked about the latter. Someone said “It’s zero”. I said, “Yes, that would be an answer.” Someone else said “two”, another said “seven” and others threw out numbers until I said “There are lots of answers which is why we call it indeterminate.” I overheard Jimmy whispering to a classmate: “We could have kept this going for a long time.”
This struck me as a fitting description of my talks—first with Ellen and then Diane—which, like the mathematical concept of zero divided by zero, seemed to be indeterminate. On the one hand they were meant to help me be a better teacher. On the other the discussions were often fueled by a chain of misconceptions and ideologies built on the magical thinking found in most ed schools. And they could go on for a long time.
But all that was ending at long last. The principal joined our final meeting which Diane started by saying “This has been quite a year for you. The seventh grade class really gave you some challenges.”
“Yes, they did,” I said. “You can lead a horse to water, as they say. But I think some of them drank it.”
“You weren’t just leading them—you dragged them to the water. Kicking and screaming,” she said. This was an exaggeration of course, but it was in my favor so I let it go.
“Any words of wisdom for us on the mentoring process?” she asked.
I’ve had the “any words of wisdom” question asked of me by HR people as part of exit interviews at other jobs I’ve had. It’s one of those questions where they want to hear good things, but are willing to take their lumps.
“I know we didn’t always agree on things,” I said.
“Yes,” she said. “It’s been interesting You’re certainly not what I expected when we first met.”
Which was probably true. I’m definitely not someone in their twenties right out of ed school. And while I had successfully avoided getting into knock-down drag outs about things like “productive struggle” and “differentiated instruction”, I did feel bad about some of our disagreements and how I had expressed them.
“In any teaching situation there are going to be people we don’t agree with,” I said with a bit of hesitation. I wasn’t sure where this was going to end up—a not unfamiliar feeling for some of my math lessons.
“Maybe we don’t agree with the way they teach or their philosophies about education. But somehow we all have to get along—we have to make it work,” I went on. “And even though I disagreed with you on some things, there were things that I did agree with and which were helpful. So that’s what I’m taking away from this.”
I don’t know if she viewed this as an apology, but I intended it as one. I could tell she meant well for me, and she had a good heart. She seemed pleased with what I said.
We then moved on to other business, signing papers, and getting instructions on how to retrieve my final teaching certificate from a certain website. And then a picture of me holding my certificate of completion.
And that was that. I was now out on good behavior as a fully credentialed teacher, free to continue putting into practice my ideas about teaching math. Free, that is, to the extent possible with having to attend PD sessions that are about engagement but pretend to be about instruction. Or hearing teachers talk about particular students’ learning styles. Or having discussions about how to instill students with a growth mindset, or being asked how I differentiate instruction in my classes, or being exhorted to engage students in productive struggle and, of course, having to be intentional. And above all: getting along with others.
I’ve been out on good behavior for over a year now and am tremendously happy at St. Stevens. As of this writing, I just completed my second year there. In keeping with my “We all have to get along” apology to Diane, I keep my views to myself.
There is the occasional PD that I have to attend, but nothing as bad as what I’ve had to endure in the past. I hear teachers talk about blended learning and intentionality and growth mindsets now and then, but we all get along. And based on my evaluation from the principal, they’re willing to look the other way.
I’m also pleased to say that Lucy, my algebra student, took algebra again in high school and got A’s all the way through. I recall during the final exam in my algebra class, she asked me for help on a point slope problem. It asked for the equation of a line passing through a point, and perpendicular to a specific line.
“I don’t know how to do this,” she said. I allowed them to have a cheat sheet and I pointed to the point slope formula that was on her cheat sheet. It was clear that my lesson deriving that formula didn’t stick with her.
A few minutes later I came back to see how she was doing. She was crying.
“Oh, you’re upset,” I said. “What’s the matter?”
She pointed to her answer to the problem.
I looked at her work. “It’s correct! You got it right.”
“But it doesn’t make sense,” she said.
I’m fairly sure she thought the problem was asking for an ordered pair of numbers. Getting an equation for an answer – well, it didn’t fit her narrative, so to speak.
And as long as we’re on the topic of “narrative”, and also in the spirit of getting along with others, I offer my readers a choice of narratives that this episode represents, with varying nuance:
1) Understanding always trumps procedures.
2) It’s all part of formative assessment.
3) At the novice level students focus on the procedure. Sometimes the understanding will come later. And for some, never.
4) Teach understanding as best as you can but don’t obsess over it.
There are probably other narratives, but I’m somewhat new at this and therefore take a rather narrow and un-nuanced view of the world. So I will leave it to my faithful readers to add their own. Just don’t tell me about them. I’m happy in my ignorance and from what I hear, doing just fine with what I know.
Editor’s Note: Chapter 20, the last chapter, will be out this Friday! This is Chapter 19 in a soon-to-be-ended series called “Out on Good Behavior: Teaching Math While Looking Over Your Shoulder” by Barry Garelick, a second-career math teacher in California. He has written articles on math education that have appeared in The Atlantic, Education Next, Education News and AMS Notices. He is also the author of three books on math education. Says Mr. Garelick: “At its completion, this series will be published in book form by John Catt Educational, Ltd. With the series almost over, the paparazzi are following me, so I’m probably looking forward to its end more than you are.” The previous chapters can be found here: Chapter 1 , Chapter 2 , Chapter 3 , Chapter 4 , Chapter 5, Chapter 6, Chapter 7, Chapter 8, Chapter 9, Chapter 10, Chapter 11, Chapter 12, Chapter 13, Chapter 14, Chapter 15 and Chapter 16, Chapter 17, and Chapter 18.
Chapter 19: An Evaluation, the Red Book, and Checking for Understanding
Marianne, the principal at St. Stevens, would occasionally do informal observations of teachers without notice. I had such an observation about the second week of the school year during my Math 7 class. As she got seated at the desk she was greeted by John, one of my students hiding underneath.
“Sometimes they like to hide from me and surprise me,” I said.
This sufficed as an explanation and gave her a window into how I run my classes. It was a good lesson and on the Data Walk-Through form she was very positive about what she saw. She didn’t mention John’s hiding underneath the desk, but later in the day a teacher told me he heard about it, so apparently word gets around quickly.
A more formal evaluation occurred later in the school year. Prior to the event, I had to fill out a form outlining my plan, stating what standards would be the focus of the lesson, and how I would “differentiate the lesson to meet the needs of all learners”. I had said that I would give the stronger students more complex problems to do. I wasn’t sure whether that would occur in class or part of their homework, but I felt my answer was good enough.
The observation occurred in my algebra class, on graphing quadratic functions. The students in that class were a noisy bunch and quite spontaneous. Earlier that year during a sudden downpour the class cheered and before I could stop them, ran outside to get soaked in the rain, including Lucy my recalcitrant student.
There was nothing to worry about for my evaluation; the students were well-behaved. I had students come up and do graphing at the board as part of the lesson, I asked questions and called on those I knew would have answers, and then called on weaker students who, I was glad to see, were able to answer as well.
After going through the lesson, I then assigned students to small groups. I did this to act in the manner that I assumed was expected of teachers aligned with the educational party line. I paired strong students with weaker ones, and gave each group an equation to graph. I circulated around to answer questions and inspect what was done.
About a week later, I met with Marianne in her office, to go over her observations of that particular lesson. She handed me her written comments while she talked to me about her observation of my class.
“I really thought that was a good lesson,” she said. “They followed the explanations, they were engaged, it was well-scaffolded, and it’s clear that they really like you.”
She offered me more praise and it was obvious from this and previous conversations with her that she thought well of what I was doing. But evaluations being what they are she then brought up her concerns.
“I notice that the textbook wasn’t used in this lesson. How are you using it? Do you use it for homework?”
I wasn’t sure whether she was asking about my use of Dolciani’s textbook or the official textbook. So I proceeded cautiously. “The lesson was actually taken from the blue textbook,” I said. (This is the official one). “I incorporate problems from the book into my lesson and yes, the homework is generally taken from the book.”
I could see that she was concerned over whether we were adhering to the Common Core standards as did public schools. I understood this—it would be bad for business if students graduating from St. Stevens would be at a disadvantage in public high schools. In her mind, sticking to the official textbook meant compliance with Common Core.
And while I had mentioned in my initial interview my extensive use of the Dolciani book in teaching algebra, I discerned that such information had not stuck with her. So I offered further clarification.
“I primarily use the book by Dolciani.”
“That’s the red book I’ve seen students with?”
“Yes. I dislike the blue book; I think Dolciani is much better.”
“But you do use the blue book?”
“Yes; to cover what isn’t addressed in Dolciani—like the lesson you saw, and pretty soon exponential functions.”
“So you’re saying you use the red book as a supplement?” she asked.
I said “Yes” even though I believe we both knew that “supplant” would have been more accurate. But people hear what they want or need to hear.
Our conference ended positively and afterward I read her written notes. She questioned how I checked for understanding, noting that I paired weaker students with stronger in my small groups. How I would assess whether the weaker could have completed the lesson without the stronger?
Excellent question; I had to agree. In acting the way I thought I was expected to act I hadn’t considered that perhaps Marianne disliked small groups as much as I do. In fact, I hate small groups. I took her question as a sign that perhaps Marianne hated them as much as I do. As far as how one checks for understanding, there are many ways. I’ve made a note that next time I’m asked, I will rely upon the ed school catechism that formative assessment is a process not an event.
She also noted that I did not do what I said I would in the pre-observation form; namely give challenging problems to the stronger students. Her recommendation: “More intentionality to provide challenge to those students that need it.” To be honest I forgot that I said I would do that.
She reiterated her concern about the textbook and recommended “Intentional correlation between lesson and text to ensure Common Core standards need for Algebra 1 mastery are adequately covered.” I’m always a bit confused about the word “intentional” as used in education. But I think I assured her that my use of text (both “red” and “blue”) was not by accident.
Supporters who want to keep Common Core’s failed standards in place have come up with a new twist for deceiving unhappy parents. First, they point explicitly to Common Core as a failed strategy to increase the academic achievement of low achievers in order to alert parents to what has happened.
They do what seems at first confusing because it is widely known that most parents and teachers (if they felt free to speak their minds) detest Common Core’s standards, tests, and aligned textbooks or readings. All Common Core’s failings and limitations are real. While the many articles on the decline in student achievement in a Common Core-aligned educational environment tell the truth, there is malice in the schadenfreude expressed about the many disadvantaged kids who have been deprived of the educational equity that Common Core was initially touted as creating.
The strong possibility of public deception is suggested by two phenomena. First, there has been no media clamor in reports of Common Core’s failures for stronger standards and curriculum materials. Second, Common Core’s major supporters—the bureaucracy at U.S. Department of Education (USED), most if not all state departments of education (e.g., DESE), and the Gates Foundation—have kept their financial and political commitment to the failed strategy. Not one major foundation, or USED, or NAEP educator has advocated that Common Core’s materials and approach be replaced with more effective ones despite their failure. The problems, they and many others claim, lie with the mandated tests—and lack of federal money. Explicitly, they don’t like “standardized” tests but think “performance-based assessments” would do the trick, even though they are costly, time-consuming, and unreliable.
Strange. State commissioners and departments of education have long known that in order to get rid of Common Core-based tests and get really different tests they must get rid of Common Core’s standards. They also know that Common Core-aligned standards and textbooks are in each state’s 4-year state education plan—all approved by the USED bureaucracy in 2016 or 2017 and that these Common Core-aligned standards MUST be used until 2020. That’s why the strategy of public deception is taking place this year.
Some states may seem to be changing their K-12 math and ELA standards right now. But what the USED bureaucracy approved for the Every Student Succeeds Act or ESSA (the Obama/Duncan administration’s title for the revision of the Elementary and Secondary Education Act, passed in December 2015 and sponsored by Senators Lamar Alexander and Patti Murray) in a state plan written in early 2016 and approved soon afterwards is in control. Every state department of education knows that, even if the public still doesn’t know who wrote ESSA and paid for it.
But ways to strengthen the K-12 curriculum are available. Most of the old pre-Common Core standards (pre-2009) are still available even if archived away (e.g. Massachusetts’ original pre-2009 standards). Or states could do what many countries like Finland have always done at the high school level: (1) create syllabi (i.e., course outlines showing content and readings to be taught) for all the courses that students are required to take in high school for their particular curriculum program (in Finland, there may be over seven to choose from) and (2) also require all students who want to go on to a 4-year college to take a “matriculation” test.
If states like Massachusetts do this, the governor or secretary of education has to ensure that the committees creating syllabi for high school courses consist of experts in both pedagogy and content, such as classroom teachers in grades 11/12 and college profs who teach math and science to freshmen in engineering schools. If high school syllabi (or standards) are created by school administrators or teachers for learning disabled or low-achieving students below grade 11, they are useless and invalid. They will be Common Core standards warmed over.
In the meantime, the Heritage Foundation seems to think that removing cabinet-level status from the USED will cure the ailments to public education inflicted on public education by the Gates Foundation. Making the USED a lower-level education agency, it claims, will enable parents to regain control of the local K-12 curriculum. How this miracle would remove the damage the Common Core project has imposed on public education is anyone’s guess. But if both “conservatives” and “liberals” support the idea, like the “lockdown,” it will happen and in another decade we will all wonder why this country chose to shoot itself in the foot.
Cross posted from New Boston Post.
Editor’s Note: This is Chapter 18 in a soon-to-be-ended series called “Out on Good Behavior: Teaching Math While Looking Over Your Shoulder” by Barry Garelick, a second-career math teacher in California. He has written articles on math education that have appeared in The Atlantic, Education Next, Education News and AMS Notices. He is also the author of three books on math education. Says Mr. Garelick: “At its completion, this series will be published in book form by John Catt Educational, Ltd. I appreciate your devotion to the series and hope you will not regret the time spent doing so.” The previous chapters can be found here: Chapter 1 , Chapter 2 , Chapter 3 , Chapter 4 , Chapter 5, Chapter 6, Chapter 7, Chapter 8, Chapter 9, Chapter 10, Chapter 11, Chapter 12, Chapter 13, Chapter 14, Chapter 15, Chapter 16 and Chapter 17.
Ch 18 An Unexpected Narrative, a Limbic Dialogue and a Note from Ellen
Having worked for forty years in both the private and public sectors prior to my retirement, I can say that the axiom I formulated in Chapter 14 applies to both the teaching and non-teaching worlds. Restated: You never know for sure what’s really going on, but general suspicions suffice to fit the narrative at hand until nuances prove otherwise.
I had kept my notice of termination at the Cypress School under wraps, having told only Diane, and one teacher who I trusted. I didn’t want the students to know. I heard stories from other teachers about receiving lay-off notices every year and getting hired back. Even the Superintendent had said that it could be rescinded.
This bolstered a vague belief that the same would happen to me. I was therefore surprised when on a Monday in May, the teacher who I had told said “I’m sorry to hear you were let go.”
Clinging to the narrative I had been given to understand, I said “That can be rescinded.”
She looked at me, and speaking rapidly, informed me of a new narrative. “Sandra has been told she will be replacing you.”
This development had occurred the previous Friday; the whole school knew but me. Sandra who taught third grade was told that she would be teaching my math classes the next year. In fact, she had taught middle school math with James a few years ago. They would be hiring a third grade teacher to replace her.
My first thought before going into limbic mode was that at least I wasn’t being replaced by Sandra’s student teacher who had observed my algebra class the previous year. “Was anyone planning on telling me?”
“The principal is in her office,” she said in very kind tones.
I took the hint and stormed into the principal’s office. By way of greeting I said “Well, I just heard that despite declining student enrollment, there’s still going to be two math teachers and I’m not one of them. What the hell does this mean?”
“Yes, sometimes people are shuffled to make things come out right.”
“Meaning what, exactly?” I asked.
The principal was a very nice woman who genuinely liked me but was not one to go against the Superintendent. “Why don’t we talk to the Superintendent about this?” she suggested.
I was in full limbic mode when we entered his office. I broke the ice.
“I have been more than professional about all of this and I am not happy that I am finding out from another teacher about Sandra taking over my job,” I said. “Why wasn’t I informed about this decision?”
“Do you think I have to share information about staff decisions?”
“Given that this affects me, I think that would be safe to say,” I said.
“Look, as I told you before, this had nothing to do with performance. I can’t go against the law though and I had to let someone go. Since you were the least senior, it was you.”
This reference to the law was interesting. I was thinking: he lets me go, moves the more expensive Sandra into my spot, gives her other assignments so she retains full time status (I was part-time), and then hires a teacher to replace her. Seems like there are just as many teachers as before and more money expended. I felt like saying “You do realize I teach math, don’t you?”
“It’s like in baseball,” he said. “They let players go with trades all the time. It’s the same here.” I said nothing. “Look, you know I think highly of you. You taught a tough class of seventh graders who love you. I was even going to make you permanent.”
This was true; he had told me that. But something happened to make him change his mind. I knew I’d never know what it was. As he went on talking, I realized it was over for me and nothing was going to change.
My limbic mode having subsided I became professional once more, like a baseball player being traded. I told him I appreciated the opportunity to vent, because it would have festered had we not had the discussion. I didn’t apologize for my initial outburst
Later as I was sitting in my classroom during lunch there was a knock on the door. It was Sandra. I had the door closed, since this was one day I didn’t want the usual group of my algebra students congregating, as much as I enjoyed them.
“I just want you to know that I had no idea you hadn’t been told what happened. I feel terrible about it,” she said. “And believe me, I really don’t want to teach math. I want to stay teaching third grade. I was told that this is what I’m going to do.”
“So you and James will be the math teachers?”
“Yes. We taught together before. I’ll be teaching algebra. We’ll both be teaching sixth grade because it’s a big class.” I could tell she felt bad about the situation. She said she was going to tell the principal she didn’t want to teach math and to be kept in her position teaching third grade. I knew that nothing would change and it didn’t.
I kept my silence about events; my students didn’t know what happened. Over the next week, with the exception of James, teachers expressed their regrets. I notified Diane and Ellen. Diane said she would be happy to be a reference. And Ellen wrote me the following note:
“I am so sorry that you have had to endure this undeserved trauma. I have worked with new teachers for 20 years and have witnessed this process over and over again. Most of my teachers have gone on and taught at other schools and never looked back.”
I would shortly be hired by St. Stevens, but in the meantime I found it oddly comforting to know that despite conflicting narratives about education, some things never change. And with that, I began the narrative of preparing my final exams.
Editor’s Note: This is Chapter 17 in a series called “Out on Good Behavior: Teaching Math While Looking Over Your Shoulder” by Barry Garelick, a second-career math teacher in California. He has written articles on math education that have appeared in The Atlantic, Education Next, Education News and AMS Notices. He is also the author of three books on math education. Says Mr. Garelick: “At its completion, this series will be published in book form by John Catt Educational, Ltd. Thanks to my faithful readers for hanging on. There are only three more chapters to go until the end.” The previous chapters can be found here: Chapter 1 , Chapter 2 , Chapter 3 , Chapter 4 , Chapter 5, Chapter 6, Chapter 7, Chapter 8, Chapter 9, Chapter 10, Chapter 11, Chapter 12, Chapter 13, Chapter 14, Chapter 15 and Chapter 16.
Chapter 17: “Math Talk”, Stalin’s Hemorrhoids, and Murder of Crows
The energy that accompanies the start of the school year begins to dwindle noticeably around Thanksgiving, continuing through the approach of Christmas. It starts up again for a short time in January. Around February or March, when the rains bring tree frogs, students (and teachers) start to sense that spring break is near with summer vacation soon following.
Seventh graders are growing and starting to look like eighth graders. And eighth graders are now looking ahead and becoming nostalgic for what will soon be a big part of their past. It is a nostalgia in advance—a holding on to the familiar at the same time as saying goodbye.
In my Math 8 class at St. Stevens, the holding on to the familiar manifested itself in even more conversations than normal. The literature on math education does not talk much about eighth graders’ conversations. I recently saw an article claiming that “research shows” that students who talk about their math thinking are motivated to learn. In addition, this “math talk” is viewed as a form of formative assessment giving teachers a peek into student thinking and where they need help.
I believe that motivation comes from proper instruction which allows students to carry out the tasks and achieve success. “Math talk” is an effective tool only if the instruction they received allows them to make use of it. Otherwise, it is like children dressing up in their parents’ clothes to play “grownups”.
As far as a peek into student thinking, sometimes the conversations pertained to the math problems they were working on—and sometimes not. But as long as they were working on math, I didn’t mind. Shortly after the tree frog incident when Jared tried unsuccessfully to find the loud croaker, I was putting my plan to teach them more algebra into high gear. I had introduced some simple factoring exercises which Jared found these fun and even said “Invigorating!” as he did them.
We were making fairly good progress with factoring, but when we got to algebraic fractions they got a bit bogged down. I had to continually remind them to factor in order to simplify.
“I don’t like factoring,” Jared said.
“Why? You told me they were invigorating a few weeks ago.”
“That was before they got complicated,” he said.
His friend Kevin chimed in. “Factoring messes things up,” he said.
“Look at it this way,” I said. “When you take algebra next year in high school, you will have seen all this already. You’ll be wondering why you thought this was difficult.”
Mary and Valerie had their own private conversations which would often merge with the others’. One particular conversation and its tributaries comes to mind. Valerie, avoiding saying the word “hell” said “H, E, double hockey sticks.”
Lou reacted to this. “There’s nothing wrong with saying the word ‘hell’. It’s a place,” he said. Discussion followed about when “hell” was permissible to say and when it was not.
“I don’t see the big deal,” Lou said.
“You would if you were Catholic,” Valerie said.
“OK, I’m not Catholic, but I believe in Jesus. I just think Catholics are too strict about some things.”
Kevin chimed in “Well, this is a Catholic school so there are certain things you have to go along with.”
“Hell shouldn’t be one of them,” Lou said though it was unclear whether he meant the concept of hell itself or about saying the word.
Kevin then asked me how to find the lowest common denominator of two algebraic fractions. As I was showing him, Mary, who clearly did not want to do any more work asked, “Lou, if I died would you cry at my funeral?”
“Well, I would be sad,” he said. “But I don’t cry easily.”
“What would it take to get you to cry?” she asked.
He appeared to be in thought. “I don’t know. When my grandmother died I didn’t cry, but when my dog died, I did. I don’t understand why.”
I had finished helping Kevin with his problem, and thought I might help Lou with his. “You don’t always cry when someone dies,” I said. “When my mother died last summer I was sad but I didn’t cry.”
“Sorry about your mom,” Valerie said.
The room grew suddenly quiet; students are listening when you least expect it.
“But then I had a dream about her one night,” I said. “And when I was telling someone about the dream, I started crying.”
“You probably cried because you knew you were saying goodbye,” she said.
Which, unbelievably was what the dream was about. I had to go somewhere but couldn’t take my mother with me so I had to say goodbye. There was no need to mention that so I didn’t and conversations returned to less somber topics—in particular, the history paper Lou was writing about Stalin. “Stalin died from hemorrhoids,” he said.
“How can you die from hemorrhoids?” I asked.
“I assume that will not be covered in your history paper,” I said, but his answer was drowned out by a noisy chorus of crows in the tree outside.
“Can I chase the crows away?” Jared asked.
“Stay seated,” I said and shut the door to the classroom.
“The door won’t block out the sound,” Jared said.
I shut the door and the crowing stopped. I said “Do you hear them now?”
Never at a loss for a rejoinder, Jared said “The motion of the door scared them away.”
“Do you have proof of that?” I asked.
He didn’t answer.
“I’ll take that as a no,” I said.
“Can we play hangman?” Jared asked.
“If you’re all finished with your math problems.”
“There’s only two minutes left of class,” he said.
I gave the go-ahead, and Lou and Jared jumped up to put their hangman challenge on the board. I realized at that moment that I had grown quite fond of this class, and that our little rituals were starting to feel like we were saying goodbye.
Editor’s Note: This is Chapter 16 in a series called “Out on Good Behavior: Teaching Math While Looking Over Your Shoulder” by Barry Garelick, a second-career math teacher in California. He has written articles on math education that have appeared in The Atlantic, Education Next, Education News and AMS Notices. He is also the author of three books on math education. Says Mr. Garelick: “At its completion, this series will be published in book form by John Catt Educational, Ltd. Please read at your own risk.” The previous chapters can be found here: Chapter 1 , Chapter 2 , Chapter 3 , Chapter 4 , Chapter 5, Chapter 6, Chapter 7, Chapter 8, Chapter 9, Chapter 10, Chapter 11, Chapter 12, Chapter 13 and Chapter 14 and Chapter 15.
Chapter 16 Instructional shifts, Formative Assessments, and Taking Matters into My Own Hands
Whenever the word “shifts” appears in an article about education, it is highly likely that what you’re reading is blather, claptrap, drivel, garbage and idiocy. (Sorry for all the adjectives; I was trying to avoid saying the word “crap”.) Even more so, if the article talks about formative and summative assessments. While formative assessment is a valid concept, its meaning may vary depending on who you talk to or what article you happen to read.
For example, formative assessment may be defined as evaluating how someone is learning material while summative assessments evaluate how much someone has learned. So says one expert. Another says summative assessments can be used formatively, by using the results to guide approaches in subsequent courses.
These hermaphroditic definitions have provided me much cover in my quest to appear aligned with whatever shiny new thing happens to be in vogue. My first parole officer, Ellen, got me started down the path of formative assessment. Although she had no shortage of suggestions for things I would never consider doing, there was one that I thought I’d try. “Have you ever let students use their notes for a quiz or test?”
I liked the idea and during my first year at Cypress, I allowed my classes to use notes for quizzes, but not tests. I felt that this would reinforce the idea of the value of notes. The problem was that some students’ organizational skills were lacking—resulting in this typical conversation:
Student: How do you do this problem?
Me: Look in your notes.
Student: I can’t find it.
Me: (Drawing a diagram on a mini-white board.) How would you find the time each of the cars are driving?
Student: I don’t know.
Me: (Writing “Distance = Rate x Time” underneath the diagram)
Such incidents led me to provide help to students in a direct manner rather than the “read my mind” approach that entails asking vague questions that serve to frustrate rather than elucidate. Sometimes I would partially work out the equation for a particular problem. Other times I would use an example of a similar problem. Expanding from a worked example to solve similar problems demands critical thought, and does exactly what math reformers pretend that unguided discovery does.
I continued this approach with my Math 7 class during my second year at Cypress. I was intent on bolstering the confidence of my students who had suffered the previous year and were convinced they could not do math. I was making headway with them using JUMP, and I could see that getting decent test scores had positive results. But as we got into more complex topics, they were having difficulty and asking for help.
I knew that there was a potential that such approach could quickly blossom into grade inflation and an artificial sense of achievement. So I justified my giving them help by telling myself that their difficulties helped guide my instruction. But I knew there were limits.
“It’s hard for me to not give help when I see they’re on the wrong track,” I told Diane during one of our sessions.
“Yes!” she said. “They have to learn from mistakes.”
Fearing a foray into Jo Boaler’s money-making “mistakes make your brain grow” motif, I rapidly changed the subject and tried out a new idea. “I’ve been thinking of giving students a choice when they ask how to do a problem, or whether it’s correct. If I answer, it will cost them points deducted from their score. I need to wean them from this dependence on my help.”
“Brilliant!” she said, took a sip of coffee and said again “That’s brilliant!”. And so I tried it. For the most part it worked. Jimmy asked if a problem were correct and I said it would cost 5 points for me to answer. “Never mind,” he said. For those students clearly lost I would not deduct points. Over time it became a judgment call—do they really need help or hand-holding?
I continued this technique and have used it at St. Stevens. It has evolved so that I will offer help as needed, but at a certain point in the school year, I will announce my policy of deducting points for certain questions.
If there are many questions in the course of a test or quiz, I find myself falling back on one of the many definitions of formative assessments, telling myself I’m using the results to guide future instruction.
My algebra class at St. Stevens was a case in point. The class was a mix of students, most of whom were able to stay afloat and do well on tests and quizzes. But there were others who perhaps should not have been placed in the algebra class who struggled and were falling behind. I would offer hints and help for those who were clearly lost. Some students would ask for help, some would not. And for those that did, they would also attempt problems on their own.
And then there was Lucy. Despite the one victory in which she was motivated enough to find a method for factoring more complex trinomials, she once again settled into her usual mode of angrily putting down answers that she thought made a kind of sense. In fact, I found that she had forgotten how to factor trinomials. She rarely asked for help during tests. I gave it to her anyway.
In keeping with summative sometimes being formative, I advised her parents that it would be best if she repeated algebra 1 in ninth grade. Lucy and her parents were receptive to this. There was one other student for whom I made the same recommendation and it was accepted, no question. Both went on to get A’s in algebra their freshmen year.
My interpretation of formative and summative assessments may not be what others think it is. Also, well-intentioned learning scientists may view me as not providing students with enough “retrieval practice”, “interleaving” and “spaced repetition”. I’ll let you look those terms up on your own. (I assure you I do all those things.) In the end, it all boils down to what used to be called “teaching”.
Editor’s note: This is Chapter 15 in a series called “Out on Good Behavior: Teaching Math While Looking Over Your Shoulder” by Barry Garelick, a second-career math teacher in California. He has written articles on math education that have appeared in The Atlantic, Education Next, Education News and AMS Notices. He is also the author of three books on math education. Says Mr. Garelick: “At its completion, this series will be published in book form by John Catt Educational, Ltd. If it is made into a movie I will be played by either Jeff Bridges or Harrison Ford. The part of Ellen will be played by Jamie Lee Curtis; Diane will be played by Helen Mirren.” The previous chapters can be found here: Chapter 1 , Chapter 2 , Chapter 3 , Chapter 4 , Chapter 5, Chapter 6, Chapter 7, Chapter 8, Chapter 9, Chapter 10, Chapter 11, Chapter 12 and Chapter 13 and Chapter 14.
Ch 15. Professional Development, Memorization, and Dubious Rubrics
As part of the parole/credentialing process, I was required to have nine hours of Professional Development (PD) for the school year. I didn’t realize it at the time, but a conference I attended prior to my starting at Cypress came in handy when it came time for my first mentor Ellen to fill in the electronic checklist on professional development (PD).
I had attended a conference given at Oxford University, sponsored by a grass-roots organization called researchED, a teacher-led organization dedicated to disseminating information on effective teaching practices backed by scientific research. I had in fact given a presentation at this conference about the state of math education in the U.S., how it got that way, and how it looked like it was going to stay there thanks to Common Core.
I asked Ellen whether I could count my attendance at the researchED conference, given that it occurred in the summer before I started at Cypress. “Of course it does,” she said. “I wish we could count it double, since you presented there.”
She didn’t ask what my presentation was about, nor did I volunteer it. In fact no one at the school ever asked. While I’d like to paint myself as a totally altruistic hero, I have to say I really wish someone had shown even the slightest interest.
“Can you describe a session that you attended?” Ellen asked.
I told her about a session on the role of memory in learning and understanding. She looked at me over her lap top.
“Memorization?” she asked.
“Memorization is not a good thing,” she said as if she were talking about parents beating their children. “Was this person advocating it?”
“It was about how memory plays a role in learning.”
This wasn’t looking good. “You taught biology, right? Did you need to know a lot of information?”
“Names of organisms, what’s in a cell, and so forth, right? Somehow that gets into your long-term memory doesn’t it?”
She started typing information into her electronic form. “OK, how does this sound?” she asked. “The session focused on long term memory and its role in understanding.”
“Sounds good,” I said. While she did not appear entirely convinced that this was true, she did look satisfied that it would pass muster by her superiors. I use the same technique. For example, if asked to describe in writing my preferred teaching style, I might say “I use direct and explicit instruction with worked examples to fulfill my intentionality of having students construct their own knowledge.”
“What other PD did you have this year?” she asked.
“This is where it gets a bit difficult,” I said. “I was required to attend a six hour session held here at the school the week before school started.”
“Why is this difficult?”
“Because I really didn’t like it. It was called ‘How to lesson design like a rock star teacher.’ “
“It was about designing lessons?”
“More or less. I guess. I don’t know. It was six hours of being all over the map, and the guy clearly didn’t like certain things.”
I stopped there. It was hard to know what to say or not say about it. There was the “ice breaker” in which the moderator—a jovial know-it-all who name dropped several constructivist leaders he admired—had us state what our “super power” is? (Why is so much PD steeped with the vocabulary that has teachers being “rock stars” or “super heroes”?) I noticed that James, the union rep said “sarcasm” which I found interesting. When the leader got to me, I said “Card magic”. Although the moderator has a rejoinder for each person’s response, he didn’t know what to say to mine, so he moved on.
There was the comparison we had to make between various instructional methods, using a scoring rubric based on Creativity, Communication, Collaboration and Critical Thinking—a textbook example of confirmation bias. Creativity was based on whether the method incorporated open ended questions with more than one answer. The moderator showed the first candidate on the screen:
My group agreed that there’s nothing wrong with a math workbook and we gave it high points, but we didn’t exactly follow the rubric either. We saw the need for practice, and felt that not everything has to be open ended or collaborative. Since there are no wrong answers in situations like these, the moderator upon seeing that we gave it a good score exclaimed “Good for you!” and then added “There’s nothing wrong with workbooks, they have their place, but you have to be aware of the potential for creativity.” Which was the edu-reform way of saying: “You really shouldn’t have given workbooks such a high rating.”
I told Ellen none of this given her educational inclinations.
“I can see that a six hour session on lesson design is a bit much,” she said. “But can you think of anything that you got out of it?” I could see she needed something positive in order to fill out her electronic form.
“Well there was one thing that made sense,” I said. “He was critical of projects like building models of the California missions out of sugar cubes, or making a model of a Navajo village, because it is not teaching anything other than the construction itself.”
“Ah, good,” she said and started typing. “How does this sound? ‘Effective lessons should reflect and reinforce what students are expected to learn about a particular subject.’ ”
“Sounds good,” I said.
I wasn’t being completely honest about this part of the PD. I neglected to tell her that after making his point about how sugar cube missions had no educational value, he told us what he thought was in fact a good activity. (Wait for it). “Minecraft!” he said.
For those who don’t know, Minecraft is a video game version of Lego blocks in which players build structures while discovering and extracting raw materials, making tools, and fighting computer-controlled mobs.
I’m not sure what rubric he was using to give Minecraft high marks, but I suspect it had to do with the “potential” for Creativity. Or words to that effect.
Editor’s note: After a long hiatus because he teaches during the school year, Mr. Garelick returns once again in presenting the fourteenth chapter in a series called “Out on Good Behavior: Teaching Math While Looking Over Your Shoulder”. Garelick is a second-career math teacher in California. He has written articles on math education that have appeared in The Atlantic, Education Next, Education News and AMS Notices. He is also the author of three books on math education. Says Mr. Garelick: “At its completion, this series will be published in book form by John Catt Educational, Ltd. Also, to my devoted readers, I decided to name the first school I taught at as Cypress School rather than “my previous school” to reduce confusion and irritation with the author.” The previous chapters can be found here: Chapter 1 , Chapter 2 , Chapter 3 , Chapter 4 , Chapter 5, Chapter 6, Chapter 7, Chapter 8, Chapter 9, Chapter 10, Chapter 11, Chapter 12 and Chapter 13.
Ch 14 Operating Axioms, the Death March to the Quadratic Formula and an Unimpressed Student Teacher
In math, assumptions held to be self-evident are accepted without proof and are called axioms. In teaching, as in many situations in life, one also makes many assumptions. I accept them without proof not because they are self-evident, but because 1) they seem like they could be true, and 2) I lack absolute proof. My axioms change from day to day depending on circumstance and observation but eventually they coalesce into a consistent set. Associated theorems then follow with the proviso that I could be dead wrong.
During my first year at Cypress I was forming many axioms particularly for my algebra class. It was a small class—only 11 students—and included two sets of twin girls. One set determined the tone of the class—they were somewhat dour and projected a “don’t mess with me” vibe. The other twins were very bright, and students clamored to be seated next to or near them whenever I changed the seating.
The class was unusually quiet and for the first few months I was always in doubt as to where I stood with them. It wasn’t until about March when we hit the chapter on quadratic equations that I felt I was hitting my stride with them.
At the start of the chapter I announced that we would now be continuing on our death march to the quadratic formula. “We’ve learned to solve some types of quadratic equations by factoring, but now were going to look at more complicated cases when we can’t factor,” I said. “By Friday of this week we will learn the quadratic formula.” I then wrote it on the board:
I tend to stay away from things like posting “Today’s Objective” since most students ignore them as do I. I find it far more effective to let them know what they’ll be doing in a week’s time, or even a month’s. Plus the looks of horror and disbelief on their faces tell me I have their attention. “By Friday this will not look as ominous to you as it does now,” I said.
And sure enough, by the time Friday came, and after working with solving quadratic equations by completing the square, they were ready for the much easier way of solving equations by the formula. After they felt comfortable with the formula I told them that next week I would show them how the formula is derived.
“What does deriving the formula mean?” one of the dour twins asked.
“It means solving the equation ax2 + bx + c = 0 using the steps of completing the square.”
“And the derivation of the quadratic formula will be an extra credit problem worth 10 points.”
“It must be hard,” the other dour twin said.
“I don’t think it’s hard,” I said. “If you can complete the square, you can derive the formula.”
“I love completing the square,” one of the bright twins said.
Earlier that week the third grade teacher, Sandra, had asked me if the student teacher she was mentoring in her class could observe one of my lessons.
“She’s interested in teaching middle school math and wants to see a class.”
“She doesn’t want to teach elementary school?” I asked.
“She’s exploring options.”
“Does she know what middle school is like?”
“I think that’s why she wants to observe a class,” Sandra said. Sandra had in fact taught algebra at Cypress a few years before, team teaching with James, the union representative. An opening for a third grade teacher came up and Sandra went for it, apparently preferring it to middle school.
“Fine,” I said. “I’m deriving the quadratic formula next Monday in my algebra class. Have her come by.”
The student teacher was in her twenties and projected an aura of confidence that comes from a belief that the (forgive me) crap ideas she had been fed in ed school were actually worth following. (I’m assuming this as an axiom and feel fairly confident in doing so.)
I started my lesson that day by pointing to a poster I had made which bore a quote from Rene Descartes: “Each problem that I solved became a rule which served afterwards to solve other problems.”
“Nowhere is this more evident in Algebra 1 than in the derivation of the quadratic formula,” I said, and proceeded to show the steps. The students knew how to complete the square, having done it as part of last week’s death march. As I worked through the derivation I asked them for the next steps. For the most part, they knew them, though it often took some prodding on my part. I note that this is how I normally teach but I was particularly aware of keeping up a dialogue lest I be judged guilty of too much “teacher talk” as traditional teaching has come to be characterized.
At the end of the class, the student teacher left without a thank you—or anything. Her head was held obnoxiously high. I assume but cannot prove that she thought that all I was doing was promoting memorization and imitation of procedures, but not “deeper understanding”.
I never heard from Sandra on what the student teacher might have thought. And in fact, I noticed that she was no longer as friendly to me as she once had been. I assume (but cannot prove) that I was somehow discredited in her eyes.
I did ask Sandra how her student teacher was doing, hoping to get some feedback. “Oh, she’s doing some innovative things in the class room,” she said. What these innovative things were she didn’t say, nor did I ask. I assume with some degree of confidence that it involved group work, collaboration, student-centered, inquiry-based projects and not answering students’ questions.
As it stands, four out of my eleven students got the derivation correct on the test. Two or three more got partial credit for getting halfway through. I hold out belief that at least one person was as fascinated as I was years ago in seeing how a method for solving problems could be turned into a formula.
I have no proof of this of course.
As a former member of the Alabama State School Board (2003-2019), I would like to share my concerns about the ballot language for Amendment One. When voters get a ballot on March 3, this is all that is printed in the ballot summary about Amendment One:
“Proposing an Amendment to the Constitution of Alabama of 1901, to change the name of the State Board of Education to the Alabama Commission on Elementary and Secondary Education; to provide for the appointment of members of the Commission by the Governor, subject to confirmation by the Senate; and to authorize the Governor to appoint a team of local educators and other officials to advise the commission on matters relating to the functioning and duties of the State Department of Education (Proposed by Act 2019-345.)”
This brief summary is misleading and totally unacceptable. This is the political equivalent of “bait and switch.” Totally missing from the ballot is the very important content of SB 397 in Section 5 beginning at the bottom of page 4 and continuing on to page 5 mandating the new commission (which replaces the current state school board) to adopt five things. The first is “Course of study standards that ensure nationwide consistency and the seamless transfer of students from within and outside the state in lieu of common core.” The ballot summary for March 3 does not include any mention of standards.
Last December before the summary for the ballot was available, a legislator contacted the Legislative Services Agency Legal Division to confirm what the ballot language would be. He was given this information: “If the Amendment passes, the (new governor-appointed) commission will have to develop new standards which “ensure nation-wide consistency and the seamless transfer of students.”
A representative of the AL State Department of Education said they were are not aware of any other nationally recognized standards for math and English Language Arts other than the Common Core Standards. Unfortunately voters would not have any way of knowing this since it’s not included on the ballot.
Any assertion that Amendment One will free Alabama of the much-detested Common Core State Standards aka College & Career Ready Standards is false. Voters who rely solely on the ballot summary will not realize that the Common Core standards will be permanently written into the Alabama constitution. We would have to pass another constitutional amendment to ever get rid of them. Although the Secretary of State’s office was asked to add necessary information from the bill onto the ballot for clarity, this was not done.
On Monday several organizations including the Alabama Farmers’ Federation (ALFA) , Forestry, Manufacture Alabama, the Alabama Realtors Association and perhaps others began running hundreds of thousands of dollars worth of ads endorsing Amendment One. The ads complain about our low test scores and how elected board members are too political. Apparently the Amendment One proponents think having a state school board made up of members who all were appointed by one person will not be “political.”
For those too young to remember or who have forgotten, many years ago the Alabama State School Board was an appointed board. However, it was changed to an elected one because the appointed board was not doing a good job. Right before the Common Core standards were implemented, former state school superintendent Joe Morton spoke frequently about how students’ scores had increased, moving Alabama up to the middle range of states. Then after a few years of using Common Core standards and assessments, our students’ scores plummeted to the bottom in math and close to the bottom in reading. I remember student progress declined all across America both in states with appointed state school boards as well as those with elected boards after the Common Core State Standards were implemented nationwide. If we are serious about improving learning, we need to start by actually replacing the much-hates Common Core aka College and Career-ready Standards with some that are more traditional and have been proven to work . Perhaps returning to the ones we were using immediately before Common Core would be a good start–at least when we were using them, our students’ performance was going in the right direction.
I know I’m not the only person who thinks there has been some legislative chicanery going on with this amendment. If the legislature and governor are so proud of it, why are they hiding so much of it, especially the information about Common Core, from the voters on election day, and why would it take so much media time to convince voters that it’s a good idea.
Link to the actual bill language which is not available on the sample ballot: https://legiscan.com/AL/text/SB397/id/2049734/Alabama-2019-SB397-Enrolled.pdf